DISCUSSION PAPER SERIES No. 10986 WHAT DO WE KNOW ABOUT FISCAL MULTIPLIERS? Carlo A. Favero and Madina Karamysheva INTERNATIONAL MACROECONOMICS AND FINANCE
DISCUSSION PAPER SERIES
No. 10986
WHAT DO WE KNOW ABOUT FISCAL MULTIPLIERS?
Carlo A. Favero and Madina Karamysheva
INTERNATIONAL MACROECONOMICS AND FINANCE
ISSN 0265-8003
WHAT DO WE KNOW ABOUT FISCAL MULTIPLIERS?
Carlo A. Favero and Madina Karamysheva
Discussion Paper No. 10986
December 2015 Submitted 03 December 2015
Centre for Economic Policy Research
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Copyright: Carlo A. Favero and Madina Karamysheva
WHAT DO WE KNOW ABOUT FISCAL MULTIPLIERS?
Abstract
The Empirical evidence on fiscal multipliers is very heterogeneous. In this paper we first survey available estimates of fiscal multipliers to try to understand their heterogeneity. We provide a general framework that allows to make the identification and specification choices made by the different authors explicit and leads hopefully to a better understanding of the heterogeneity of results.
JEL Classification: E62 and H60 Keywords: fiscal adjustment, fiscal plans and output growth
Carlo A. Favero [email protected] Deutsche Bank Chair, IGIER‐Bocconi and CEPR Madina Karamysheva [email protected] Bocconi University
What Do We Know About Fiscal Multipliers?
Carlo Favero and Madina Karamysheva∗
November 2015
Abstract
Keywords: fiscal adjustment, output, fiscal plans
Abstract: The Empirical evidence on fiscal multipliers is very het-
erogenous. In this paper we first survey available estimates of fiscal
multipliers to try to understand their heterogeneity. We provide a gen-
eral framework that allows to make the identification and specification
choices made by the different authors explict and leads hopefully to a
better understanding of the heterogeneity of results
1 Introduction
Fiscal multipliers measure the output effect of fiscal adjustments. This is
undoubtedly a controversial issue. Different theoretical models give very
different predictions on the magnitude and the sign of the effect of fiscal
adjustment on output and other macro variables (see, for example, Baxter
and King,1993, De Long and Summers 2012, Christiano et al. (2011). The
empirical evidence has produced a plethora of different estimates (see Ramey,
2015). This survey concentrates on the empirical evidence and it is aimed
at understanding its heterogeneity. We review the available literature by
analyzing the design of the relevant empirical experiment that allows the
measurement of multipliers.
Our tenet is that the role of empirical analysis of fiscal policy is to estab-
lish the evidence relevant to select the theoretical model capable of matching
∗Carlo Favero: Deutsche Bank Chair, IGIER-Bocconi, and [email protected]., Madina Karamysheva: Phd student Boccony Uni-versity [email protected]. Paper prepared for the confer-ence "Rethinking Fiscal Policy After the Crisis", Bratislava September 2015. Wethanks, without implicating them, our discussant, Michal Horváth, and conferenceparticipants for comments and suggestions
1
it. Policy simulation analysis should then be implemented by using the se-
lected relevant model.
It is well understood by now that the validity of experimenting with
reduced form empirical models requires that a number of conditions are sat-
isfied. First, empirical reduced form models need to be simulated by keeping
all parameters constant, in fact estimated parameters in reduced form model
might depend on the parameters determining the economic policy rules. Sim-
ulating alternative parameterizations of the rules requires a structural model
while simulating deviations from the rules, whilst keeping their systematic
component constant, makes the empirical evidence robust to the Lucas (1972)
critique. However, deviations from the rules must satisfy further conditions
(Ramey 2015) for the investigator to be able to make valid inference on their
effect: (i) they must be exogenous for the estimation of the parameters of
interest,(ii) they must be uncorrelated with other relevant structural shocks
so that their effect can be assessed by keeping all the other shocks constant
and the causal effect of deviations from the rule can be uniquely identified,
(iii) they must be unanticipated because the relevant response of agents to
discriminate among models is the one to modifications in their information
sets.
We argue that the relevant experiment to measure multipliers is to con-
sider deviation from fiscal rules that come in the form of multi-year correc-
tions: fiscal adjustment plans. Fiscal adjustment plans are a series of multi-
period correlated one-period corrections (shocks). They describe closely the
way in which deviation from fiscal rules are currently implemented by policy
makers.
Plans consist of the announcement of a sequence of fiscal actions, some to
be implemented the same period of the announcement (unanticipated) and
some to be implemented in following periods (announced). Plans are also
a mix of measures on government expenditures and revenues. The design
of plans generates intertemporal and intratemporal correlations among fiscal
variables. The intertemporal correlation is the one between the announced
(future) and unanticipated (current) components of a plan. The intratem-
poral correlation is that between the changes in revenues and spending that
determines the composition of a plan.
Traditionally the empirical fiscal literature concentrates on shocks. Inter-
estingly plans nest shocks and taking the perspective of plans will allow us
to write down a general empirical model and derive virtually all the different
specifications adopted as special cases of this model. The general "nesting"
empirical model that we will set up is too heavily parameterized to be esti-
mated empirically but it is useful in that it allows to the evaluate the different
identification and specification strategies adopted in the literature as choices
2
on the relevant dimensions of the empirical models and therefore to put
the heterogeneity of the findings in the empirical evidence in a more general
context.
In the next section we will describe exactly how plans are designed and
how the most general empirical model can be constructed, we shall then
assess the available literature in terms of the restrictions imposed on such a
general model.
In a fourth section we shall give an illustration of the relevance of different
strategic choices on the measured multipliers.
The last section concludes.
2 A general framework
In this section we build a general framework to describe the empirical evi-
dence on fiscal multipliers. Such a framework is constructed in two steps:
the identification of the relevant experiment and the specification of the
empirical model to assess its effects.
2.1 The Relevant Experiment: Fiscal Stabilization Plans
The analysis of the output effects of economic policy requires — for the correct
estimation of the relevant parameters — identifying policy shifts that are
exogenous. If the object of interest is the output effect of fiscal stabilization
measures, then exogeneity of the shifts in fiscal policy for the estimation of
their output effect requires that they are not correlated with news on output
growth.
Fiscal policy is conducted through rare decisions and it is typically imple-
mented through multi-year plans: modelling a standard set of US variables
with a medium-scale structural model that allows for foresight up to eight
quarters, Schmitt-Grohe and Uribe (2012) find that about 60% of the vari-
ance of government spending is due to anticipated shocks. A fiscal plan
typically contains three components: (i) unexpected shifts in fiscal variables
(announced upon implementation at time t), (ii) shifts implemented at time
t but announced in previous years, and (iii) shifts announced at time t, to
be implemented in future years. Consider, for simplicity, the case in which
the forward horizon of the plan is only one year with reference to a specific
country i, and assume that corrections exogenous for the estimation of the
parameters of interest can be observed. An exogenous plan can be described
as follows:
3
= + 0 + 1 = + +10 = 11 = 1
+ 1 1 = 2
+ 2
1 = 3 + 3 1 = 4
+ 4
= 5 + 5
(1)
Total fiscal corrections in each year consist of increases in taxes and cuts
in expenditures. Unexpected shifts in fiscal variables by the fiscal authorities
in country are labeled respectively and We define and
the tax and expenditure changes announced at date with an anticipation
horizon of years (i.e. to be implemented in year + ). Finally, 0 (0)
denotes the tax (expenditure) changes implemented in year that had been
announced in the previous years. The fiscal plan is completed by making
explicit the relation between the predictable and the unpredictable compo-
nents and the taxation and the expenditure components. The parameters
1 to 5 pin down the intratemporal and the intertemporal correlations
of the different components of the fiscal plan. Note the framework allows
for modifications of an announced measure upon implementation recording
them as an unexpected shift in policy.
2.2 The Empirical Model
Simulation of plans requires to embed them in a dynamic model for macro-
economic variables. We consider, for the sake of illustration, an a over-
parameterized general model that does not have a sufficient number of degrees
of freedom to be estimated but nests most of the specification considered in
the empirical literature so far. The main purpose of this general model is
to make explicit the specification and identification choices adopted by the
different authors. Consider modelling the macroeconomic impact of fiscal
policy in i countries as follows
z = 1 ( ) z−1 +2 ( ) z∗−1 +3 ( ) −1 (2)
+1 () +2 ()
+ 1 ()
0 + 2 ()
0 +
+1 () 1 +2 ()
1 + u
=1 +
(1 + )−1 +
()− ()()
(3)
≡ ∆ +∆ +∆∆
u ∼ (0Σ)
4
= + 0 + 1 = + +10 = 11 = 1
+ 1 1 = 2
+ 2
1 = 3 + 3 1 = 4
+ 4
= 5 + 5
where z is the vector of domestic macro variable that, in order to be
able to dynamically simulate (3) must include the average nominal cost
of financing the debt , ∆ real GDP growth, ∆, inflation, and are,
respectively, government revenues and government expenditure net of inter-
est.
From (3) it is immediately obvious that the dynamics of the debt is fully
determined at any point in time by the dynamics of a subset of the variables
included in the vector z moreover the relationship between the debt and
the variables in z is non-linear.
Several comments on this specification are in order.
1) The endogenization of the debt-deficit dynamics allows to check that
impulse response functions are not computed of diverging paths for fiscal
fundamentals. The explicit inclusion of in the dynamic model allows
to pin down explicitly the debt stabilization motive in the fiscal reaction
function and the impact of debt in the macro dynamics
2) The coefficients in the dynamic macro model depend on a regime
For example in a Smooth Transition VAR for z only the regime switch is
modelled as follows:
z = (1− (−1))1 () z−1 + (−1)1 () z−1 + uu ∼ (0Σ)
Σ = Σ(1− (−1)) + Σ (−1)
() =exp(−)
1 + exp(−) 0
() = 1 () = 0
where is an observable (standardized) index of the business cycle.
3) Foreign variables z∗ are allowed to have an impact.4) Fiscal plans are modelled as described in the previous section and, for
simplicity, the foresight horizon is limited to one-period. Exogenous fiscal
plans are observable and they are available to the econometricians
5) Heteroscedasticity is allowed in the component of fiscal plans and in
the model residuals.
5
6) The model is non linear but impulse responses can be computed as the
difference between two forecasts:
( ) = (z+ | = ; )− (+ | = 0; ) = 0 1 2
Once impulse response are available multipliers, as argued by Mount-
ford and Uhlig (2009), Uhlig (2010) and Fisher and Peters (2010), can be
calculated as the integral of the output response divided by the integral gov-
ernment adjustment (spending or taxation) response.
3 Empirical Models
The available contribution in the literature can be discussed by classifying
them according to the restrictions they impose on the general structure de-
scribed in the previous section.
3.1 Early SVAR Models
The early studies of the macroeconomic impact on fiscal variables concentrate
on shocks by neglecting the intertemporal nature of fiscal plans. therelevant
policy shift are identified with shocks. However, The analysis of the output
effects of economic policy requires — for the correct estimation of the relevant
parameters — identifying policy shifts that are exogenous. Exogeneity of the
shifts in fiscal policy for the estimation of their output effect requires that
they are not correlated with news on output growth. The traditional steps to
identify such exogenous shifts were to first estimate a joint dynamic model
for the structure of the economy and the variables controlled by the policy-
makers (typically estimating a VAR). The residuals in the estimated equation
for the policy variables approximate deviations of policy from the rule. Such
deviations, however, do not yet measure exogenous shifts in policy because
a part of them represents a reaction to contemporaneous information on the
state of economy. In order to recover structural shocks from VAR innova-
tions some restrictions are required. So empirical models can be classified
via the restrictions they impose on the specification and the identification
restrictions.
3.1.1 Traditional SVAR
Blanchard and Perotti (2002) (BP) is the traditional benchmark for the lit-
erature of VAR-based investigation of the output effect of fiscal policy:
6
BP specify the following restricted model to measure fiscal multipliers:
⎡⎣ 1 0 −130 1 −23−31 −32 1
⎤⎦⎡⎣
⎤⎦ = 1 ()
⎡⎣ −1−1−1
⎤⎦+⎡⎣ 12 0
21 0
0 0
⎤⎦⎡⎣
⎤⎦where and are the log of real quarterly taxes, spending and
GDP all in real per capita terms. Taxes are net taxes defined as the sum of
Personal Tax and Non tax Receipts, Corporate Profits Tax Receipts, Indirect
Business Tax and Non tax accruals, Contributions for Social Insurance less
Net Transfer Payments to Persons and Net Interest Paid by the Government.
Government Spending is defined as Purchases of Goods and Services, both
current and capital. Data are quarterly and seasonally adjusted for the period
1947:1 to 1997:4. The 0 are non observable mutually uncorrelated structuralshocks normalized to be of variance 1. However, they can be identified by
imposing some restrictions on the 0 and the 0 Estimate a reduced formVAR in the three variables of interest, the VAR residuals 0 will be relatedto the 0 as follows:
⎡⎣ 1 0 −130 1 −23−31 −32 1
⎤⎦⎡⎣
⎤⎦ =
⎡⎣ 12 0
21 0
0 0
⎤⎦⎡⎣
⎤⎦u = e
from which we can derive the relation between the variance-covariance
matrices of u (observed) and e (unobserved) as follows:
(uu0) = A−1B (ee
0)B
0A−1
= A−1BB0A−1 = CC0 = Σ
Substituting population moments with sample moments we have:
dX= bA−1bBIbB0 bA−1, (4)
cP contains ( + 1)2 different elements (where n is the dimension of the
VAR), which is the maximum number of identifiable parameters in matrices
A and B. Therefore, a necessary condition for identification of the structural
shocks is that the maximum number of parameters contained in the two
matrices equals (+1)2 such a condition makes the number of equations
equal to the number of unknowns in system . As usual, for such a condition
7
also to be sufficient for identification no equation in (4) should be a linear
combination of the other equations in the system.
As there are 9 parameters in the BP model at least three identifying
restrictions are needed. First, BP rely on institutional information about
tax, transfer and spending programs to restrict the parameters 13 and 23
These coefficients, in quarterly data, are assumed to exclusively driven by the
automatic effects of economic activity on taxes and spending and they are
restricted to the output elasticities of government purchases and net taxes.
Using information on the feature of the spending and tax and transfer system
BP set 13 = 208 23 = 01The last restrictions is obtained by considered
two alternative scenarios, 12 = 0 and 21 = 0that are observed to have a
negligible impact on the final results.
The identification restrictions are combined with the specification re-
strictions on the general model. Namely, only one country is considered
(US), the vector of variables z consists only of three variables, con-
stant parameters are assumed 1 ( ) = 1 () no foreign vari-
able enter the specification 2 ( ) = 0, there is no explicit debt feed-
back 3 ( ) = 0 and the debt dynamics is not modelled, plans are
not introduced and shocks are combination of announced, unanticipated
and anticipated corrections which are restricted to have the same effect
1 () = 1 () = 1 () = 1 2 () = 2 () = 2 () = 2
Impulse response are then computed andmultipliers are calculated by first
multiplying the estimates by the sample mean of government spending and
net taxes to GDP ratios, and then by comparing the peak output response
to the initial government spending or tax impact effect. Note that this is
different from computing the integral multipliers described in the previous
section.
Two sets of empirical results are reported generated respectively by al-
lowing for stochastic trends (and specifying the model in first differences)
or by considering a specification in level with deterministic trends. The Tax
multiplier is around one (-1.33 in the ST against -0.78 under DT) and similar
in size to the spending multiplier ( 0.90 in the ST against 1.29 under DT).
Some evidence of subsample instability emerges. Follow-up work, such as by
Fatas-Mihov(2001), Perotti(2005), Pappa(2005) and Gali, Lopez-Salido and
Valles(2007), found similar results.
The BP specification is very restrictive: the set of variables considered
is very limited, the model does not allow for debt feedback and tracking of
the debt dynamics and identified shocks are convolution of unanticipated,
1Caldara(2011) shows that the sensitivity of estimated multipliers to changes in these
elasticities can be very large.
8
anticipated and announced corrections. The first set of restrictions have not
been extensively debated in the literature, the second set can be rationalized
by considering that the US debt dynamics has never deviated from stability
and therefore the model can be thought of as including a linearized version of
the identity driving the debt dynamics. However, Leeper (2010) stresses the
importance of avoiding analyses of “unsustainable fiscal policies” and of mak-
ing sure that the question "What is the fiscal multiplier" is not asked along
a path for the debt dynamics that is at odds with the beliefs of government
bond-holders.
As a matter of fact the restrictions that has elicited more debate is the
one that implies that identified shocks to government spending and taxa-
tion are anticipated. Ramey (2011a, b) argues that distinguishing between
announced and unanticipated shifts in fiscal variables, and allowing them
to have different effects on output, is crucial for evaluating fiscal multipli-
ers. Leeper et al.(2013) illustrates explicitly that fiscal foresight makes the
number of shocks to be mapped out of the VAR innovations is too high to
achieve identification: technically the Moving Average representation of the
VAR becomes non-invertible (see also Lippi and Reichlin(1994)).
3.1.2 SVAR with sign restrictions
Mountford and Uhlig(2009) (MU) apply to the analysis of fiscal policy the
methodology originally introduced by Uhlig(2005) to identify monetary pol-
icy shocks. MU represents the VAR of interest as follows
z =
X=1
Az− + u
u = Ce
Σ = CE (ee0)C
0 = CC0
Consider now as the Cholesky decomposition of Σ.
The impulse response function, given the Cholesky decomposition could
be written as :
z = [I−A ()]−1CeAll the possible rotations of the Cholesky decomposition are obtained as
follows:
[I−A ()]−1CQQ0eQQ0 =
9
The impulse response for Q0e is then [I−A ()]−1CQThe imposition of the sign restrictions then considers Q to generate all
possible identification and then select only those that satisfy some restriction
on their sign.
The vector y contains many more variables than the corresponding one
in BP; in fact Mountford-Uhlig specify a VAR in GDP, private consumption,
total government expenditure, total government revenue, real wages, pri-
vate non-residential investment, interest rate, adjusted reserves, the producer
price index for crude materials and the GDP deflator. These 10 variables are
considered at a quarterly frequency from 1955 to 2000, the VAR has 6 lags,
no constant or a time trend, and uses the logarithm for all variables except
the interest rate which is specified level. The definition of the two fiscal
variables is the same with BP. Sign restrictions are used to identify shocks of
interest. (i) A business cycle shock is defined as a shock which jointly moves
output, consumption, non-residential investment and government revenue in
the same direction for four quarters following the shock2; (ii) A monetary pol-
icy shock, which is taken to be orthogonal to the business cycle shock, moves
interest rates up and reserves and prices down for four quarters after the
shock iii) fiscal policy shocks are orthogonal to business cycle and monetary
policy shocks, government spending shocks and government revenue shocks
are identified by a positive response of the corresponding variables such re-
sponse is restricted to be delayed (to take into account fiscal foresight) and
permanent (to rule out temporary fiscal adjustment).
If we interpret MU in terms of our general model they take a close econ-
omy, constant parameters approach, they restrict 1 = 2 = 0 they do not
track separately the response upon announcement and upon implementation
and they impose the restrictions that all the parameters are positive, ex-
cept those determining the cross correlation between revenue and expenditure
adjustments, that are set to zero.
The tax multiplier (deficit-financed tax cuts) is almost three times larger
than that computed by BP and stands at 3.57 (with a peak effect after 13
quarters) while the deficit-spending multiplier is slightly lower than that of
BP as it stands at 0.65 (with a peak effect upon impact). Interestingly,
by linearly combining their two base fiscal policy shocks MU analyze also
the effect of a balanced budget tax cut. Comparing these three scenarios,
they find that a surprise deficit financed tax cut is the best fiscal policy
2Note that this restrictions implies that when output and government revenues move in
the same direction, this must be due to some improvement in the business cycle generating
the increase in government revenue, not the other way around.
10
to stimulate the economy, giving rise to a maximal present value multiplier
of five dollars of total additional GDP per each dollar of the total cut in
government revenue five years after the shock.
3.1.3 Expectational VARs
Expectational VARs try and solve the problems posed by fiscal foresight and
endogeneity by constructing an instrument for fiscal corrections using infor-
mation outside the VAR. Ramey and Shapiro (1998) use narrative techniques
to create a dummy variable capturing military buildups. Business Week is
used as a source to isolate political events the led to buildups exogenous to
the current state of the economy, the narrative approach was also used to
make sure that the relevant shocks were unanticipated. The effect of the
"war dates" was measured by estimating single equations for each variable
of interest including current value and lags of the war dates and lags of the
left hand side variable.
To understand this approach consider the structural representation of a
constant parameter closed economy first-order VAR:
Az = Cz−1 +Be (5)
The MA representation of (5) is
z = Γ()e (6)
where Γ() ≡ A−1BI−A−1C . The MA representation is not directly estimated
in the VAR, but it can be derived by inversion, after having estimated (5)
We re-write (6) as follows
z =
X=0
Γ0Γ1e− + Γ+1
1 z−(+1)
Γ0 ≡ A−1B Γ1 ≡ A−1C
and extract from the above system the equation for a variable of interest,
say output growth
∆ =
X=0
− +
X=0
− +
X=1
X=0
− (7)
+Γ+11 z−(+1)
11
where
= sΓ0Γ
1s
0 = 1
s =£1 0 0 0 0
¤ s =
£0 1 0 0 0
¤s =
h0 0 1
2+0
i
Consider now the relation between the true unobservable expenditure
shocks and the narrative instrument
=
+ (8)
∼ ¡0 2
¢i.e.. assume that the difference between the expenditure shocks in the VAR
and those identified via the narrative method is some error This assump-
tion has a number of testable implications, in particular should be
orthogonal to all the lags of all the variables included in the VAR.
We can now write
∆ =
X=0
− +
X=0
− + (9)
+
X=0
− +
X=1
X=0
−
+Γ+11 z−(+1)
(9) makes clear that the limited information approach adopted by Ramey
and Shapiro in which the variable of interest is regressed on a distributed
lag of the instrument and lags of the left hand side since variables can be
interpreted as a simplified version of (9) that omits variables that are thought
of as orthogonal to the regressors (i.e. the distributed lags of other shocks
and the measurement error). Within this framework of interpretation there is
a potential problem related to the omission of lags M+1 and longer of all the
other variables in the dynamic system. This omission is the less problematic
the more the system is stationary and the inclusion of lags of the dependent
variable might be thought of as a way of swamping this effect.
To overcome the limited information approach a number of follow-up pa-
pers (Edelberg, Eichenbaum, and Fisher (1999), Burnside, Eichenbaum, and
Fisher (2004), and Cavallo 2005) embedded in a VAR by ordering them
12
first in a Cholesky decomposition. Fisher and Peters(2010) created an alter-
native forward looking series of news based on the excess returns of defense
contractor shocks for the period starting in 1958. These applications typi-
cally found that government spending with a multiplier in the range 0.6-1.5
and therefore slightly higher than that of BP, but comparable especially after
taking into account the effect of fiscal foresight in BP type models. Ramey
(2011a) showed that the shocks from an SVAR were predictable by
After correcting for this effect, the obtained impulse responses become more
similar. Barro, Redlick(2011) also use military build-ups as an instrument
for defense spending but they also include in the specification a measure for
marginal tax rate and allow for non-linearities making the effects of revenue
and expenditure shocks function of unemployment. Their estimated multi-
plier for defense spending is 0.6-0.7 at the median unemployment rate (while
holding fixed average marginal income-tax rates) rising in unemployment to
reach 1 when the unemployment rate is around 12 per cent. Increases in
the average marginal income-tax rates have a significantly negative effect on
GDP with an implied magnitude of the multiplier of 1.1.
3.2 Narrative Measures
Romer and Romer(2010) (R&R) proceed to non-econometric, direct identi-
fication of the shifts in fiscal variables. These are then plugged directly into
an econometric specification capable of delivering the impulse response func-
tions that describe the output effect of fiscal adjustments. In this “narrative”
identification scheme a time-series of exogenous shifts in taxes or govern-
ment is constructed using parliamentary reports and similar documents to
identify the size, timing, and principal motivation for all major fiscal policy
actions. Legislated tax changes are classified by R&R into endogenous for
their estimation of their output effect (induced by short-run countercycli-
cal concerns) and exogenous (responses to an inherited budget deficit, or to
concerns about long-run economic growth or politically motivated). R&R
construct time-series for the US considering quarterly observation over the
period 1945:1-2007:1. There is an interesting fact about the two type of
exogenous tax changes which is evident from the following figure reported by
R&R. The deficit-driven tax changes are almost exclusively positive (episode
of fiscal expansion motivated by inherited surplus are virtually non existent)
while all the long-run tax changes are negative (i.e. expansionary).
If the perspective of plans is adopted to interpret the R&R narrative
identification we can classify their tax shocks as the sum of corrections an-
nounced at time t and immediately implemented (therefore unanticipated)
and corrections announced at time t to be implemented in future periods:
13
Figure 1
= + 1
The effect of tax shocks is then measured by running the following single-
equation specification.
∆ ln = +() + (10)
So a truncated constant parameter single country MA representation is
adopted, where only the exogenous components of tax adjustments is consid-
ered with the restrictions that unanticipated and announced corrections have
the same effect and announced corrections have no impact upon implementa-
tion. The resulting evidence is that tax increases are highly contractionary :
a tax increase of 1% of GDP has a cumulative effect of a reduction of output
over the next three years of nearly 3 %.
The narrative approach has been extended to the UK case by Cloyne
(2013) who constructs a new narrative dataset of legislated tax changes in
the UK, to apply the R&R empirical approach and find that a 1 percentage
point cut in taxes as a proportion of GDP causes a 0.6 percent increase in
GDP on impact, rising to a 2.5 percent increase over nearly three years.
Devries et al (2011, D&al) extend the narrative approach to a multi-
country sample that identify episodes for 17 OECD countries between 1978
and 2009. These authors concentrate on deficit driven corrections to revenue
and expenditure that are not compensated by long-run corrections. Adopting
the perspective of plans the Devries et al corrections are constructed by
adding up two components: unexpected shifts in fiscal variables occurring
14
in year (that is announced when they are implemented), and shifts in
fiscal variables which also occur in year but had been announced in previous
years, 0
= + 0
= +
0 = 0 + 0
Guajardo et al (2014) have used these data to estimate fiscal multipliers
using constant parameters panel data techniques on the international sample
(and therefore by imposing the restrictions 1 = 1 2 = 3 = 0 1 =
1 2 = 21 = 2 = 0) . In practice, in their baseline specification, they
estimate the following panel version of the single equation model adopted by
R&R:
∆ = +1()∆−1 +1() + + +
where denotes country fixed effect and denote year fixed-effects.
They estimate that the effect of a 1 per cent of GDP fiscal consolidation
has a contractionary effect on GDP with a peak effect of -0.62 per cent within
two years (t-stat=-3.82).
3.2.1 The Government Intertemporal Budget Constraint
Leeper(2010) states clearly that "...Fiscal policy will shed its alchemy label
when the question “What is the fiscal multiplier?” is no longer asked and
detailed analyses of “unsustainable fiscal policies” are no longer conducted
without explicit analysis of expectations and dynamic adjustments ...".
The traditional VAR literature takes sustainability for granted and inter-
prets the estimated VAR as linearized model around a stable debt/GDP path.
Chung and Leeper(2007) impose this equilibrium condition on an identified
VAR and characterize the way in which the present-value support of debt
varies across various types of fiscal policy shocks and between fiscal and non-
fiscal shocks. Favero and Giavazzi(2012) propose an extension of the standard
VAR model augmented with observable narrative tax adjustments, ca-
pable of explicitly tracking the dynamics of debt/GDP in response to fiscal
shocks.
The following empirical specification is introduced for estimating tax mul-
tipliers
15
z =
X=1
Cz− + δ + γ (−1 − ∗) + u (11)
=1 +
(1 +∆) (1 +∆)−1 +
exp ()− exp ()exp ()
z0 =
£ ∆
¤where Z includes the five variables present in a fiscal VAR. Debt is explic-
itly introduced in the VAR. The estimated model on US data never delivers
"unsustainable debt paths" and the model augmented with debt and the
non-linear debt dynamics equation produces results which are very similar
to those obtained by including the R&R shocks in a traditional fiscal VAR.
U.S. data are drawn from a sustainable fiscal regime: within this regime it
is likely that the feedback between fiscal variables and the (linearized) debt
dynamics is captured in a linear VAR specification that includes all the vari-
ables that enter in the debt-deficit relationship. Nevertheless, having the
possibility of checking that fiscal multipliers are computed along a sustain-
able path is an important step, that might become relevant for countries
other than the US.
Corsetti, Meier and Muller(2012) analyze the effects of an increase in gov-
ernment spending under a plausible debt stabilizing policy that links current
stimulus to a subsequent period of spending restraint. They show that ac-
counting for such spending reversals of crucial importance to bring standard
new Keynesian model in line with the stylized facts of fiscal transmission.
3.2.2 External Instrument SVARs
Mertens and Ravn(2013, 2014) propose to consider the series based on the
narrative evidence as a noisy measure of the true unobservable fiscal shock.
They identify exogenous tax changes in a VAR model by proxying latent tax
shocks with narratively identified tax liability changes.
Given a VAR in n variables consider again the relationship between the
variance covariance of the observed VAR innovations u and the unobserved
structural shocks e :
u = e
(uu0) = A−1B (ee
0)B
0A−1
= A−1BB0A−1 = CC0 = Σ
16
Substituting population moments with sample moments we have:
dX= bA−1bBIbB0 bA−1, (12)
cP contains ( + 1)2 different elements (where n is the dimension of the
VAR), which is the maximum number of identifiable parameters in matrices
A and B.
Consider now the availability of a vector of × 1 observable proxyvariables that are correlated with the structural shocks of interest e1 and
orthogonal to the other − shocks e2 ( where e0 = [e
01 e
02]). The proxy
variables have zero mean and satisfy two conditions:
(e01) = Φ (e
02) = 0 (13)
where Φ is an unknown nonsingular × matrix.
Consider the following partitioning of C
=h1
2(−)
i1 =
∙ 011
021
(−)
¸02 =
∙ 012
(−) 022
(−)(−)
¸0with nonsingular 11 and 22. Conditions (13) together with the relation
between structural shocks and VAR innovations imply that
Φ 01 = Σ0 (14)
This system, which is of dimension × , provides additional identifying
restrictions but it also depends on the 2 unknown elements ofΦ. If one is not
prepared to make any further assumptions on Φ other than nonsingularity,
equation (14) provides really only ( − ) new identification restrictions.
Partitioning Σ0 =£Σ01Σ02
¤, where Σ01 is × and Σ02 is ×(−)
and using (14), these restrictions can be expressed as
21 =³Σ−101
Σ02
´011 (15)
which is a viable set of covariance restrictions as³Σ−101
Σ02
´can be
estimated.
In practice, estimation can proceed in three stages
17
• Estimate the reduced form VAR by least squares.
• Estimate³Σ−101
Σ02
´from regression of VAR residuals on
• impose (15) and estimate the objects of interest, if necessary in combi-nation with further identifying assumptions.
Mertens and Ravn (2014) apply this methodology to the standard BP
VAR to reconcile the apparently different size of multipliers obtained in BP
and R&R, while Martens and Ravn (2013) discriminate between the effects
of changes in average personal income tax rates and the effects of changes
in average corporate income tax rates to find that unanticipated changes in
either tax rates produce large short run effects on aggregate output. More-
over, tax revenue falls in response to cuts in personal income taxes while on
average there is a little impact on tax revenues of the corporate income tax
cuts.
3.2.3 The Average Treatment Effect of Fiscal Policy
Jorda-Taylor (2013) reinterpret fiscal multipliers in the logic of the measure-
ment of treatment effects.
Consider a very simplified version of our general model which includes
the narratively identified fiscal correction episodes:
z = z−1 + β1 +
The MA if the VAR truncated at lag h is
z+ = +1z−1 +β1 + +
+ = β1+ + +−1β1
+1 +
++ ++−1 +
The impulse response describing the effect of the fiscal correction on the
variable of interest, say output growth, is then
¡+ − p
= 1 ¢− ¡+ − p
= 0 ¢=
X=0
∆+
=
X=0
β1
where is a selector vector that extracts output growth for the vector
of variables z This impulse response can be obtained via a series of h
18
regressions by applying the Linear Projection method introduced by Jordà
(2005)
+ = 0z−1 + + +
in practice the conditioning set z−1 can be augmented in LPM as LPM is
based on a single equation estimation (after the identification of the shocks)
and more degrees of freedom are available:
+ = 0w−1 + + +
Note also that the LP method also can easily accommodate non-linear im-
pulse responses. The comparison of the LPM regression with the full trun-
cated MA representation makes clear that LPM omits all structural shocks
between time t and time t+h. This omitted variables problem would not
lead to inconsistent estimates of the parameters of β1 ( limˆ
= 1)
only if were orthogonal to all omitted variables, or if w−1captures the
relevant variation in all omitted variables.
The use of LPM to derive IR and multipliers leads naturally to interpret
the effect of fiscal policy as the effect of a treatment. In fact the average
policy effect on a variable at horizon + can be written as
[(+ ()− )− (+ (0)− ) | ] =
Where is the policy intervention. Jorda-Taylor note that if the fiscal
corrections are to be considered as a treatment, then it is crucial that the
policy intervention is not predictable to avoid a standard allocation bias
problem. As a matter of fact are predictable by their own past, and
by past values of debt dynamics (see also Hernandez da Cos and Moral-
Benito(2011)). To solve this problem JT propose to apply LPM after having
purged the fiscal actions from predictability. They proceed as follows:
(i) redefine innovations as a 0/1 dummy variable,
(ii) estimate a propensity score deriving the probability with which a
correction is expected by regressing it on its own past and predictors,
(iii) use the propensity score to derive an Average Treatment Effect based
on Inverse Probability Weighting.
Denote the policy propensity score () = 1 0 (the predicted
values from a probit projections of the policy indicator on the set of predictors
).
= [(+ (1)− )− (+ (0)− ) | ]
=
∙(+ − )
µ1 { = 1}1 ()
− 1 { = 0}1− 1 ()
¶|
¸19
ˆ
=1
X(+ − )
ˆ
ˆ
=1 { = 1}ˆ1
()
− 1 { = 0}1− ˆ
1
()
In the LP framework ATE can be combined with LP in the following
estimator LP-IWPRA estimator
ˆ
=1
X∙( − )
ˆ
−ˆ
¡
¢¸
ˆ
=1 { = 1}− ˆ
1
()
ˆ1
()
−1 { = 0}−
µ1− ˆ
1
()
¶1− ˆ
1
()
where ¡
¢is the mean of ( − ) predicted by the LP
By applying the corrected estimator they find and average treatment
effect of fiscal consolidation which is not very different form the one estimated
by DeVries et al. with a peak effect in year 5 after the consolidation slightly
larger than -1, and a cumulative effect after five years at about -3.
To understand this evidence two remarks are in order. First exogeneity
in dynamic time-series models is different from predictability. The correct
estimation of the effects on output of a fiscal adjustment within our speci-
fication requires the use exogenous fiscal shocks, i.e. shocks that cannot be
predicted from past output growth, predictability from past shocks or other
variables not directly related to output growth is irrelevant to determine the
required exogeneity status. This requirement is satisfied by the original IMF
shocks. It is no longer satisfied, however, if one transforms those continuous
shocks into a 0/1 dummy variable, as in the paper quoted at the beginning.
The reason, as a simple regression shows, is that transformation into a 0/1
dummy, and the loss of information it implies, introduces correlation with
past output growth. Notice that the exogeneity required to estimate fiscal
multipliers within a dynamic model is different from deriving the effect of a
treatment randomly assigned, what matters in our model is weak exogene-
ity for the estimation of the parameters of interest rather then the random
assignment of a treatment.
As a matter of fact the DV corrections can be predicted from past debt
dynamics and from their past history by construction. They are predictable
by debt dynamics as they are defined as shifts in fiscal policy, ’motivated by
20
the objective of stabilizing or reducing the debt ratio’. Predictability in this
sense is not inconsistent with exogeneity with respect to past output growth:
for this reason Romer and Romer (2010), for instance, include tax shocks
motivated by the objective of stabilizing or reducing the debt among their
exogenous (for the estimation of the output effect of fiscal policy) shocks.
They are predictable from their past as these corrections are built adding
up two components: unexpected shifts in fiscal variables occurring in year
(that is announced when they are implemented), and shifts in fiscal
variables which also occur in year but had been announced in previous
years, 0 . Dropping the country index
= + 0
Based on this definition, the fact that the are correlated across time
is not surprising.
A fiscal plan is specified by making explicit the relation between , 0
and the fiscal corrections announced in year for years + ( 1). Therefore
1 = + (16)
+10 = 1 (17)
The first equation describes the style with which fiscal policy is imple-
mented. Plans along which shifts in fiscal variables are persistent will feature
a positive value of ; while temporary plans (i.e. plans along which fiscal
actions are reversed, at least partially in the future) feature a negative .
The second relationship simply states that the announced correction imple-
mented at time is equal to the correction that had been announced in the
previous period with a fiscal foresight of one period.
Then
¡
−1¢=
¡¡ + 0
¢¡−1 + −10
¢¢=
¡−1
¢as
0 = −11 = −1 + −1
However, in a dynamic time-series model, the requirement for valid esti-
mation and simulation are respectively weak and strong exogeneity, that are
different from predictability.
21
To illustrate the point consider the following simplified example:
∆ = 0 + 1 + 1
=
−1 + 2µ12
¶∼
∙µ0
0
¶
µ11 1212 22
¶¸The condition required for
to be weakly exogenous for the estimation
of 1 is 12 = 0 which is independent of When weak exogeneity is satisfied
the existence of predictability does not have any effect on the consistency of
the estimate of 1 of course neglecting the existence of predictability of
under simulation might lead to consider scenarios that were never observed
in the data and therefore to unreliable results.
3.2.4 Fiscal Plans
A natural alternative approach to deal with the predictability of the
corrections is to specify a dynamic specification for the variable of interests
and the fiscal plans.
Martens and Ravn (2011) take a first step in this direction by studying
the different effects of announced and unanticipated adjustments but they do
so without modelling the interdependence between these two components.
Alesina, Favero and Giavazzi (2014, AFG ) use the fiscal consolidation
episodes identified by Devries et al (2011), but propose a methodological
innovation. They start from the observation that the shifts in taxes and
spending that contribute to a fiscal adjustment almost never happen in iso-
lation: they are typically part of a multiyear plan, in which some policies
are announced well in advance, while other are implemented unexpectedly
and, importantly, both tax hikes and spending cuts are used simultaneously.
Also, as these plans unfold, they are often revised and these changes have
to be taken into account as they constitute new information available to
economic agents. AFG stress the importance of modelling the connections
between changes in taxes and expenditures, and between unanticipated and
announced changes. In practice they consider a restricted version of the
general model in which a quasi-panel is estimated allowing for two types of
heterogeneity: within-country heterogeneity in the effects of Tax-Based(TB)
and Expenditure-Based(EB) plans, and between-country heterogeneity in the
style of a plan
22
∆ = +1() ∗ +2()
∗ + (18)
1()0 ∗ + 2()
0 ∗ +
+
3X=1
∗ +
3X=1
∗ + + +
1 = 1 + 1
2 = 2 + 2
3 = 3 + 3
0 = −11 = −1+1 +
¡ − −1+1
¢ > 1
à + 0 +
X=1
!
à + 0 +
X=1
! = 1 = 0
= 0 = 1∀
where and are country and time fixed effects. A moving average rep-
resentation for the variable of interest ∆ is considered in (18) with no debt
feedback and constant parameters. Cross-country restrictions on the
and coefficients are imposed, but within- and between-country heterogene-
ity is allowed for. "Within" because responses of ∆ to fiscal adjustments
will be different for TB and EB plans. "Between" because they will also differ
across countries as the 0 differ, according to each country’s specific style.The dynamic effect of fiscal adjustment plans is different across countries
because of the different styles of fiscal policy (as captured by the different
) and within countries as a consequence of the heterogenous effects of plans
as determined by their composition. The moving average representation is
truncated because the length of the () and () polynomials is limited
to three-years. The moving-average representation is specified to allow for
different effects of unanticipated and anticipated adjustments. Shifts in fiscal
policy affect the economy through three components. First, unanticipated
changes in fiscal stance, , announced at time and implemented at time
; second, the implementation at time of policy shifts that had been an-
nounced in the past, 0; third, the anticipation of future changes in fiscal
policy, announced at time , to be implemented at a future date, for
= 1 2 3 Also different coefficients are allowed for adjustment announced
23
in the past and implemented at time and adjustments announced at time
for the future. To avoid double counting lags of future of are excluded, as
their dynamic effect is captured by +0 The parameters are estimated
on a country by country basis on the time series of the narrative fiscal shocks.
Note that introducing total adjustment with different labeling (TB or EB)
rather than introducing separately in the specification adjustments in rev-
enue and in expenditure allows a much more parsimonious parameterization
of the dynamic system defining the style of fiscal plans, making estimation
viable.
The system is put at work in AFG to simulate the effect of TB and EB
average plans on macroeconomic variables. Simulation of fiscal plans adopted
by 16 OECD countries over a 30-year period supports the hypothesis that the
effects of consolidations depend on their design. Fiscal adjustments based
upon spending cuts are found much less costly, in terms of output losses,
than tax-based ones and have especially low output costs when they consist
of permanent rather than stop and go changes in taxes and spending. The
difference between tax-based and spending-based adjustments appears not
to be explained by accompanying policies, including monetary policy. It
is mainly due to the different response of business confidence and private
investment.
Alesina et al. (2015) use the system to perform out of sample simula-
tions of the austerity plans adopted by different countries over the period
2009-2013. Model projections of output growth conditional only upon the
fiscal plans implemented since 2009 do reasonably well in predicting the total
output fluctuations of the countries in our sample over the years 2010-13 and
are also capable of explaining some of the cross-country heterogeneity in this
variable.
3.3 Non-linearities
Non-linearities in fiscal multipliers are investigated in a number of papers.
Corsetti, G., A. Meier and G.Mueller (2012b) study the determinants of
government spending multipliers by investigating how the fiscal transmission
mechanism depends on three dimension of economic environment: the ex-
change rate regime, the level of public debt and deficit, and the presence of
a financial crisis. The analysis is implemented on annual data for 17 OECD
countries within a sample period 1975—2008. A two-step approach is consid-
ered. In the first step the fiscal policy rule, which links government spending
and macroeconomic variables, is identified and estimated. The parameters
in fiscal policy rules are country-specific and fiscal policy shokcs are iden-
24
tified as the innovations in the rules. In a second step fixed-effects panel
regression are estimated to trace the impact of the estimated government
spending shocks on the relevant macroeconomic aggregates (output, private
consumption, investment, trade balance, real effective exchange rate). To
study non-linearities interaction terms of shocks with dummies capturing
the exchange rate regime, the state of public finances, and the presence of
financial crisis) are included in the regression. The estimated system can be
represented as follows:
g = + + 1−1 + 2−2 + 1−1 + 2−2 + −1 + −1+−1 + 1−1 + 2 + 3−1 + ε
z = + + z−1 + 1b + 2b−1 + 3b−2 + 4b−3 + 1(b ∗ ) ++2(b−1 ∗ −1) + 3(b−2 ∗ −2) + 4(b−3 ∗ −3) + 1 + 2−1 +
+3−2 + 4−3 + u
where is government spending variable, −1 −2 - lags of log percapita output, −1 lag of a composite leading indicator which measuresthe expectation with respect to next-year growth, −1 debt to gdp ratio.−1 is a dummy for an exchange rate, - is a dummy for strainedpublic finances, and −1 is a financial crisis dummy. ε - is a fiscalpolicy shock which measures discretionary policy change. The methodoolgy
does not allow to disentangle unanticipated corrections from announced and
implemented, furthermore it is assumed that innovations in the projections
of goverment spending on past information are orthogonal to deviations of
all other macroecononomic variables (including government revenues) from
their projections. z - is the macroeconomic variable of interest, b is anestimated fiscal shock from the first stage and - is a dummy for specific
economic conditions in the particular year. Importantly parameters mea-
sure the baseline dynamic effect of the spending shocks, while measures
additional marginal effects.
Corsetti, G., A. Meier and G.Mueller (2012b) model is multi country
economy, however 2 ( ) = 0,since foreign variables are not allowed to
have an impact. z is not a vector of variables of interest, but it denotes
one variable of interest at a time (output, private consumption, private fixed
investment, trade balance, the real effective exchange rate, CPI inflation, the
short-term nominal interest rate, and government spending itself). There is
no debt feedback 3 ( ) = 0. Debt dynamic is also absent in the model.
The model does not uses plans, but relies instead on general spending shocks
identified by imposing some (strong) restrcitions in the first stage regression.
25
There are three sources of non-linearities: exchange rate regimes, the state
of public finances, and the state of the economy.
Baseline results feature persistency in government spending shocks and a
sizeable response of aggregate output by about 0.7 percentage points. Under
the currency peg multipliers are positive: impact and maximum is 0.6. Weak
public finance produce negative multipliers, both impact -0.7, maximum 0.2
and cumulative after two years -1.2. The most quantitatively relevant results
are for the case of financial crisis: the responses of output to a public spending
increase is strongly positive, implying a fiscal multiplier of 2.3 - impact and
2.9 - maximum.
Auerbach, Gorodnichenko (2012) make an attempt to assess how the size
of fiscal multipliers vary over the cycle by estimating regime-switching SVAR
models, with smooth transitions across the relevant states of the economy
(i.e., recession versus expansion).
The basic adopted specification is:
z = (1− (−1))1 () z−1 + (−1)1 () z−1 + uu ∼ (0Σ)
Σ = Σ(1− (−1)) + Σ (−1)
() =exp(−)
1 + exp(−) 0
() = 1 () = 0
where z = [ ] following Blanchard and Perotti (2002) is gov-
ernment purchases, government receipts of direct and indirect taxes net of
transfers to businesses and individuals, is gross domestic product. All vari-
ables are in logs and are deflated. Estimation uses quarterly data. Structural
shocks are identified form VAR innovations by assuming lower triangularity
in the matrix that maps shocks into innovations. Importantly, the model al-
lows for both contemporaneous differences in propagation of structural shocks
as well as dynamic. The first one goes through Σ and Σ, while the second
one goes through 1 () and 1 (). is an index, normalized to have
mean of zero and variance of 1, indicating recessions if is negative and
expansion if is positive. Auerbach, Gorodnichenko (2012) set to a seven
quarter moving average of the output growth rate. is calibrated to 1.5,
which means that the economy spends around 20 percent of the time in re-
cession ( () 08) = 02. Under the assumption that 0, 1 ()
and Σ characterizes the economy in expansion and 1 () and Σ - in
recession.
26
Auerbach, Gorodnichenko (2012) model is a single country a closed econ-
omy model, the vector z consists of three variables: , there are
two states of the economy, expansion where 1 ( ) = 1 () and Σ =
Σ(1− (−1)) with (−1) = 0 versus recession 1 ( ) = 1 () and
Σ = Σ (−1) with (−1) = 1. There is no debt feedback 3 ( ) =0. The model does not uses plans, but relies instead on shocks restricting
announced, unanticipated and anticipated corrections to have the same ef-
fect 1 () = 1 () = 1 () = 1 () 2 () = 2 () = 2 () =
2 (). In alternative to the basic model a more advanced specification is
considered. This specification include professional forecasts of the relevant
variable in the vector z = [∆−1 ∆
−1 ∆ −1 ]
Because of non-linearities the estimation as well as the inference is im-
plemented using the Monte Carlo Markov Chain method with Hastings-
Metropolis algorithm, where the parameters estimates as well as confidence
intervals are computed directly from the generated chains. Computed multi-
pliers are interpreted as indicating how by how many dollars output increase
over time if government expenditure increases by $1. The size of the shock
is chosen in such a way that the integral of government spending response
over 20 quarters is equal to one.
Baseline results show that in all cases linear, expansion and recession the
impact output multiplier is around 0.5 in response to 1$ spending increase.
However, after 20 quarters under the recession regime the multiplier is 2.5
and under expansion regime the multiplier is -1. Average multiplier under
the recession is 2.24 and under the expansion -0.33. Fiscal policy is consid-
erably more effective in recessions than in expansions. This evidence refers
to polar cases, as in the computation of impulse responses the initial regime
is maintained constant: the policy innovation cannot cause a shift in
Ramey, Owyang and Zubairy(2013) remove this restrictions by comput-
ing regime-dependent multipliers using the Linear Projections (LP) method
of Jordà(2005). In LP non-linearities are easily accommodated and there is
no need to impose the restrictions that shock do not affect the state of the
economy. A state-dependent model is estimated in which impulse responses
and multipliers depend on the average dynamics of the economy in each
state. They address the question of the relevance of non-linearities by an-
alyzing new quarterly historical U.S. data covering multiple large wars and
deep recessions. Differently from previous studies they do not find higher
multipliers during times of slack in the US.
Ramey and Zubairy(2014) extend the investigation to consider the effect
of two potentially important features of the economy: (1) the amount of
slack and (2) whether interest rates are near the zero lower bound. The
main findings indicate no evidence that multipliers are different across states,
27
whether defined by the amount of slack in the economy or whether interest
rates are near the zero lower bound.
Caggiano et al.(2015) also estimate non-linear VARs and address fiscal
foresight by appealing to sums of revisions of expectations of fiscal expen-
ditures. Their results, based on generalised impulse responses that allows
a feedback from the simulated policy to the probability of the economy be-
ing in expansion and recession, suggest that fiscal spending multipliers in
recessions are greater than one, but not statistically larger than those in ex-
pansions. However, non-linearities arise when focusing on ‘extreme’ events,
that is, deep recessions versus strong expansionary periods.
3.4 Quasi Natural Experiments and Descriptive Evi-
dence.
All the literature that we have been discussing so far fits in the general
framework as all the empirical models adopted can be considered of specific
cases of our general "encompassing" model, however there are exceptions that
exploit "case studies" without specifying a dynamic model. Such studies are
best interpreted as focusing on some direct measure of the causal effect of
fiscal policy on output growth.
Acconcia, Corsetti and Simonelli (2013) exploit the introduction of a law
issued to fight political corruption and mafia infiltration of city councils in
Italy that has caused episode of large, temporary and unanticipated fiscal
contractions arguably exogenous for the estimation on their effect on output.
Using these episodes as instruments, while controlling for national monetary
and fiscal policy and keeping the tax burden of local residents constant, the
output multiplier of spending cuts at provincial level is estimated in the range
1.2-1.8.
Alesina and Ardagna(2010), adopting an approach introduced by Giavazzi
and Pagano(1990), consider a case study of large changes in fiscal policy
stance, namely large increase or reduction of budget deficits and analyze their
effects on both the economy and the dynamics of the debt. In particular,
they concentrate on episodes of large changes in fiscal policy. They use a
panel of 20 OECD countries with annual data over the sample 1970-2007.
Fiscal variables are cyclically adjusted by considering the difference between
a measure of the fiscal variable in period t computed as if the predicted value
from a regression of the fiscal policy variable as a share of GDP on a constant
a time trend and the unemployment rate, where the unemployment rate at
time t is kept at the value observed in time t-1. A period of fiscal adjustment
(stimulus) is a year in which the cyclically adjusted primary balance improves
28
(deteriorates) by at least 1.5 per cent of GDP.
Focussing on these episodes and using mainly descriptive evidence they
find that tax cuts are more expansionary than spending increases in the cases
of a fiscal stimulus, fiscal adjustments based upon spending cuts and no tax
increases are more likely to reduce deficits and debt over GDP ratios than
those based upon tax increases. Finally, adjustments on the spending side
rather than on the tax side are less likely to create recessions.
The two very different approaches adopted by Acconcia et al.(2013) and
Alesina and Ardagna(2010) have in common the direct analysis of episodes
without the specification of a dynamic macro-model. The case of the exogene-
ity of the chosen episodes for the measurement of the relevant phenomenon is
certainly much stronger in the Acconcia et al.(2013) case. In fact, Guajardo
et al.(2011) argue convincingly that changes in cyclically adjusted fiscal vari-
ables often include non-policy changes correlated with other developments
affecting economic activity. For the sake of illustration they consider a boom
in the stock market, such a boom creates a cyclically adjusted surplus by in-
creasing capital gains and cyclically adjusted tax revenues. This surplus can
be associated with an increase in consumption and investment generated by
the stock market boom. The resulting measurement error is likely to bias the
analysis towards downplaying contractionary effects of fiscal consolidations.
However, even if the exogeneity of the episodes considered by Acconcia
et al. is clearly robust to this type of considerations, the question on how
the results produced in the case studies can be extended to the measure-
ment of fiscal multipliers in presence of different dynamics, initial conditions
and heterogeneity in the mechanism of formation of expectations remains
unsolved.
4 The Impact of Different Identification and
Specification Strategies. An illustration
To illustrate the relevance of different specification choices we consider quar-
terly US data over the period 1978:1 2012:4 and compare the BP SVAR
approach with a dynamic model of fiscal adjustment plans. We use NIPA
variables described in the Appendix. To be as close as possible to Blanchard,
Perotti (2002) we use their definitions of the variables3.
3From NIPA tables: output is nominal GDP (NIPA 1.1.5.1); government spending
is General Government consumption expenditures and gross investment (NIPA 1.1.5.21);
total tax revenue is General Government Current receipts (NIPA 3.1.1) less General Gov-
ernment Current Transfers to persons (NIPA 3.1.21) less General Government Interest
Payments to persons (NIPA 3.1.25) plus General Government Income receipts on assets
29
The BP specification is the following one :
⎡⎣ 1 0 −2080 1 0
−31 −32 1
⎤⎦⎡⎣
⎤⎦ = 1 ()
⎡⎣ −1−1−1
⎤⎦+⎡⎣ 0 0
21 0
0 0
⎤⎦⎡⎣
⎤⎦where [ ] is a vector of quarterly taxes, spending, and output.
All variables are in the logarithms and in real, per capita, terms. e =
[
] are structural shocks, orthogonal to each other with. 1 () is
a lag polynomial with the length of four quarters. Following Blanchard,
Perotti 2002 we include constant, linear and quadratic trends into the model.
Sample period is 1978q1 to 2012q4. Since our sample starts with the first
quarter of 1978 we do not need to include a dummy variable for the second
quarter of 1975 as in Blanchard, Perotti 2002. BP identifying restrictions
are imposed on the matrices relating the unobserved structural shocks to the
VAR innovations.
Results are reported in the form of impulse response functions. Note
that a unit shock to the structural innovations of taxes transforms to less
than a unit change in the reduced form tax residuals, because output falls in
response to the tax increase and in turn tax revenue falls. Figure 2 reports
impulse responses where impulse response of output has an interpretation of
the tax (expenditure) multipliers, i.e. dollar changes in GDP as a ratio of the
dollar changes in tax revenues (expenditure). Following BP multipliers are
obtained by expressing impulse responses as shares of average gdp with initial
impulse normalized to 1% of average gdp. Unless mentioned otherwise, we
provide one standard deviation confidence intervals that are computed using
a bootstrap algorithm with 1000 replications. The solid line gives the point
estimates, while the dotted lines are confidence bounds.
Insert Figure 2
the BP model produces response of output insignificant and close to zero
in response to the 1% of structural tax shock . There is a negative response
of output in the short run and positive in the long run in response to 1% cut
of structural expenditure innovations.
We compare this impulse response with those obtained from a truncated
MA in a model with plans. Plans for quarterly data are reconstructed for
the US on the basis of DeVries et al. in Favero, Karamysheva(2015). In
(NIPA 3.1.8). All series are deflated by GDP deflator (NIPA 1.1.9.1) and by FRED Pop-
ulation (Midperiod, Thousands, Quarterly, Seasonally Adjusted Annual Rate).
30
the wording of R&R we consider only deficit driven plans and we adopt the
following empirical model to assess their effects
∆ = +1()( + ) ∗ +2()(
+ ) ∗ +
+1()( + ) ∗ + 2()(
+ ) ∗+
+P
=1
(+ + +) ∗ +
P=1
(+ + +) ∗ + u
u ∼ (0Σ)
(+ + +) ∗ = ( + ) ∗ + 1+ = 1
(+ + +) ∗ = ( + ) ∗ + 2+ = 1
(19)
∆ is the growth rate of GDP (quantity index for real GDP, data source
National Income and Product Accounts (NIPA) - table 1.1.3).
The specification generalizes the MA adopted by Romer and Romer by
allowing different coefficients on the unanticipated expenditure, and rev-
enue, adjustments (announced at time t and implemented at time t), on
the anticipated correction currently implemented (announced before time t,
and implemented at time t) and on the future corrections (announced
at time t, to be implemented in the future),+ +. The length of the
polynomials 1() 2() 1() 2() - is set to 6. The anticipating hori-
zon is set by considering the median implementation lag, which is again six
quarters. The MA representation is then augmented by a number of auxiliary
equations that capture the nature of the plan via the correlation between the
intertemporal and intratemporal component of fiscal adjustments.
and are dummies that label plans into Expenditure Based or
Taxed Based according to the larger present value of the types of correction.
Results are in the form of the impulse response functions, which are
obtained by forward simulation of the model. Since our dependent variable
is in differences, we report cumulative impulse response functions. The length
of the IRF is limited to the number of lags included into the system. One
Standard deviation confidence intervals are built by bootstrap with 1000
replications . We use block bootstrap to take into account potential serial
correlation in residuals, restricting the length of the block to 2. Working
with the quarterly data we give a shock of 1% to the total plan. To do
so we give initial shock to unanticipated component of the plan TB plan -
0.58%, and for unanticipated component of EB plan - 0.79%. Sample period
is from 1978 quarter one to 2012 quarter four. Figure 3 shows the responses
of output growth to the TB and EB plans.
Insert figure3
31
A positive shock to the tax based plan produces a significantly negative
effect on the output growth. While the shock to the expenditure based
plan gives a marginally significant exapnsionary effect. These results are
very different from those obtained by applying the BP method on the same
data-set with the difference being generated by different identification and
specification strategies.
5 What Have We Learned ?
This paper represent an attempt to answer to the question "What do we
know about Fiscal Multipliers?" by setting up a general "encompassing"
model flexible enough to consider all the different empirical specifications
adopted in the literature as specific cases that can be derived by imposing
set of restrictions on the general model. This framework allows us to take
into account of two crucial remarks on the empirical analysis of fiscal policy
made by Ramey(2015) and Leeper(2010). First, the measurement of fiscal
multipliers is a question for which dynamics are all-important, general equi-
librium effects are crucial, and expectations have powerful effects. Second,
multipliers depend on the type of spending or tax change, as well as on a
host of other factors: expected sources and timing of future fiscal financing,
whether the initial change in policy was anticipated or not, how monetary
policy behaves, what is the state of cycle when the policy is implemented.
There is not such a thing as a unique fiscal multiplier and the evidence ob-
tained by a specific investigation on the multiplier can be understood only
within a general dynamic framework which clearly indicates the specification
and identification choices made in that investigation.
6 References
Acconcia A., G. Corsetti and S.Simonelli (2013) "Mafia and Public Spend-
ing: Evidence on the Fiscal Multiplier from a Quasi-Experiment" The Amer-
ican Economic Review 104 (7), 2185-2209
Alesina A. and R. Perotti (1997) "The Welfare State and Competitive-
ness" American Economic Review 87, 347-66
Alesina A. and S. Ardagna (2010), “Large Changes in Fiscal Policy: Taxes
versus Spending”, Tax Policy and the Economy, vol. 24, 35—68, edited by
J.R. Brown.
Alesina A., S. Ardagna, R. Perotti and F. Schiantarelli (2002), “Fiscal
32
Policy, Profits and Investment”, American Economic Review, 92(3), 571—
589.
Alesina, Alberto, Carlo Favero and Francesco Giavazzi (2014), “The out-
put effects of fiscal stabilization plans”, forthcoming in Journal of Interna-
tional Economics, available at http://igier.unibocconi.it/favero
Alesina A., O. Barbiero, C.Favero, F.Giavazzi andM.Paradisi(2014) "Aus-
terity in 2009-2013", paper prepared for 60th panel meeting of Economic
Policy, October 2014
Auerbach A. and Y. Gorodnichenko, (2012), “Measuring the Output Re-
sponses to Fiscal Policy”, American Economic Journal: Economic Policy,
4(2), 1—27.
Bachmann R. and E. Sims, (2011),“Confidence and the Transmission of
Government Spending Shocks”, NBER Working Paper No. 17063, National
Bureau of Economic Research, Inc.
Barro R. J. and C. J. Redlick (2011), “Macroeconomic Effects from Gov-
ernment Purchases and Taxes”, The Quarterly Journal of Economics, 126(1),
51—102.
Ben Zeev, N. and Pappa, E. (2014). ‘Chronicle of a war foretold: the
macroeconomic effects of anticipated defense spending shocks’, mimeo, Eu-
ropean University Institute.
Baxter M. and R. G. King (1993), “Fiscal Policy in General Equilibrium”,
American Economic Review, 83(3), 315—334.
Blanchard O. and R. Perotti (2002), “An Empirical Characterization of
the Dynamic Effects of Changes in Government Spending and Taxes on Out-
put”, Quarterly Journal of Economics, 117(4), 1329—1368.
Blanchard, Olivier, and Daniel Leigh (2013), “Growth Forecast Errors
and Fiscal Multipliers,” IMF Working Paper No. 13/1 (Washington: Inter-
national Monetary Fund).
Beetsma R., J.Cimadomo, O.Fortuna, M.Giuliodori (2014) “The Confi-
dence Effects of Fiscal Consolidations”, paper presented at the 60th Eco-
nomic Policy Panel
Bloom N. (2009), “The Impact of Uncertainty Shocks”, Econometrica,
77(3), 623—685.
Caggiano G., E. Castelnuovo, V. Colombo and G. Nodari (2015) "Esti-
mating Fiscal Multipliers: News from a Non-Linear World", The Economic
Journal, 125, 746-776
Caldara, Dario (2011), "The Analytics of SVARs: A Unified Framework
to Measure Fiscal Multipliers," IIES working paper,
Cavallo, Michele (2005), “Government Employment Expenditure and the
Effects of Fiscal Policy Shocks,” Federal Reserve Bank of San FranciscoWork-
ing Paper 2005-16,
33
Christiano, L. J., Eichenbaum, M., and Evans, C. L. (1998). ‘Monetary
Policy shocks: what have we learned and to what end?’. NBER working
paper No. 6400.
Christiano, L., M. Eichenbaum and S. Rebelo (2011), "When is the Gov-
ernment Spending Multipliers Large?", Journal of Political Economy, 119
(1), 78-121.
Chung H. and E.M. Leeper(2007) "What has Financed Government Debt?"
NBER Working Paepr No W12345
Cloyne, J. (2013), “Discretionary Tax Changes and the Macroeconomy:
New Narrative Evidence
from the United Kingdom”, The American Economic Review, 103(4):
1507-1528.
Corsetti, G., A. Meier and G.Mueller (2012), "Fiscal Stimulus with Spend-
ing Reversals”, The Review of Economics and Statistics, 94, 4: 878-895.
Corsetti, G., A. Meier and G.Mueller (2012b), "What Determines Gov-
ernment Spending Multipliers", Economic Policy, 523-564
de Cos, Pablo Hernandez and E. Mora (2012), "Fiscal Consolidations and
Economic Growth". working paper, Banco de Espana.
DeLong J. B. and L. H. Summers (2012), “Fiscal Policy in a Depressed
Economy ”, Working Paper.
Drautzburg T. and H.Uhlig (2013) "Fiscal Stimulus and distortionary
taxation", mimeo
Dell’Erba, Salvatore, ToddMattina and Augustin Roitman (2013), “Pres-
sure or Prudence? Tales of Market Pressure and Fiscal Adjustment,” IMF
Working Paper No. 13/170 (Washington: International Monetary Fund).
Devries, Pete, Jaime Guajardo, Daniel Leigh and Andrea Pescatori (2011),
“A New Action-based Dataset of Fiscal Consolidations.” IMFWorking Paper
No. 11/128 (Washington: International Monetary Fund).
Eggertsson, G. B. (2010), "What Fiscal Policy is Effective at Zero Interest
Rates?", NBER Macroeconomic Annual, D. Acemoglu and M. Woodford
(eds), Chicago University Press.
Eggertsson, Gauti B., and Paul Krugman (2012), “Debt, Deleveraging,
and the Liquidity Trap,” Quarterly Journal of Economics, 127(3): 1469—513.
Fatás, Antonio and I. Mihov (2001) ”The Effects of Fiscal Policy on
Consumption and Employment: Theory and Evidence”, mimeo, INSEAD
Favero, Carlo and Francesco Giavazzi (2012), “Measuring Tax Multipli-
ers: the Narrative Method in Fiscal VARs”, American Economic Journal:
Economic Policy, 4(2): 69-94.
Favero C., F.Giavazzi and J.Perego (2011) "Country Heterogeneity and
the International Evidence on the Effects of Fiscal Policy", IMF Economic
34
Review, 59,4, 652-682
Fisher, Jonas D.M., and Ryan Peters (2010), “Using Stock Returns to
Identify Government Spending Shocks,” The Economic Journal, 120 (May
2010): 414-436.
Galí J., J. D. López-Salido and J. Vallés (2007), “Understanding the
Effects of Government Spending on Consumption”, Journal of the European
Economic Association, 5 (1), 227—270.
Garratt A., K. Lee, M. H. Pesaran and Y. Shin (2012), Global and Na-
tional Macroeconometric Modelling: A Long-Run Structural Approach Ox-
ford University Press.
Giavazzi F. and M. Pagano (1990), “Can Severe Fiscal Contractions Be
Expansionary? Tales of Two Small European Countries ”, NBER Chapters
in NBER Macroeconomics Annual 1990, vol. 5, 75-122.
Giavazzi F. and M. McMahon (2013), "The Household effects of Govern-
ment Spending", in A. Alesina and F. Giavazzi (eds.), Fiscal Policy After
the Great Recession, University of Chicago Press and NBER, 2013
Guajardo, Jaime, D. Leigh, and A. Pescatori (2014), “Expansionary Aus-
terity? International Evidence”, Journal of the European Economic Associ-
ation, 12(4): 949-968.
Hernandez da Cos P. and E.Moral-Benito(2011) "Endogenous Fiscal Con-
solidations", Working Paper 1102, Banco de Espana
Jalil A.(2012), "Comparing Tax and spending Multipliers: it is all about
controlling for monetary policy" mimeo, Dept of Economics, Reed College
Jordà, Oscar (2005), “Estimation and Inference of Impulse Responses by
Local Projections”, American Economic Review, 95(1): 161-182
Jordà, Òscar and Alan M. Taylor (2013), "The Time for Austerity: Es-
timating the Average Treatment Effect of Fiscal Policy," NBER Working
Papers 19414, National Bureau of Economic Research, Inc.
Leeper E. M. (2010), “Monetary Science, Fiscal Alchemy”, NBER Work-
ing Papers No. 16510, National Bureau of Economic Research, Inc.
Leeper E. M., T. B. Walker and S.-C. Yang (2013), “Fiscal Foresight and
Information Flows”, Econometrica 81(3) 115-1145
Lippi M. and L. Reichlin (1994), “VAR Analysis, Non Fundamental Rep-
resentations, Blaschke Matrices”, Journal of Econometrics, 63(1), 307—325.
Mertens K. and M. O. Ravn (2011), “Understanding the Aggregate Ef-
fects of Anticipated and Unanticipated Tax Policy Shocks”, Review of Eco-
nomic Dynamics, 14(1), 27—54.
Mertens K. and M. O. Ravn (2013), "The Dynamic Effects of Personal
and Corporate Income Tax Changes in the United States", The American
Economic Review , 103,4, 2012-47
35
Mertens, Karel, and Morten O. Ravn(2014)., “A Reconciliation of SVAR
and Narrative Estimates of Tax Multipliers,” Journal of Monetary Economics
68: S1-S19.
Mountford, Andrew and Harald Uhlig(2009), “What are the Effects of
Fiscal Policy Shocks? Journal of Applied Econometrics 24 : 960-992.
Perotti, Roberto [2008]: “In Search of the Transmission Mechanism of
Fiscal policy"; NBER Macroeconomic Annual.
Perotti, Roberto (2013), “The Austerity Myth: Gain without Pain”,
in Fiscal Policy after the Financial Crisis, edited by Alberto Alesina and
Francesco Giavazzi. (Cambridge, MA: National Bureau of Economic Re-
search)
Perotti R (2013), "The Austerity Myth: Gain without Pain?" forthcom-
ing in A. Alesina and F. Giavazzi (eds.) Fiscal Policy After the Great
Recession, University of Chicago Press and NBER.
Ramey, V. (2011a), “Identifying Government Spending Shocks: It’s All
in the Timing.” Quarterly Journal of Economics 126 (1): 1-50.
Ramey V. (2011b), “Can Government Purchases Stimulate the Econ-
omy?”, Journal of Economic Literature, 49(3), 673—685.
Ramey V. (2013), "Government Spending and Private Activities" in A.
Alesina and F. Giavazzi (eds) Fiscal Policy after the Great Recession Uni-
versity of Chicago Press and NBER forthcoming
Ramey, V., Owyang and S. Zubairy (2013), "Are Government Spending
Multipliers Greater During Periods of Slack? Evidence from 20th Century
Historical Data, American Economic Review, Papers and Proceedings forth-
coming
Ramey, Valerie A. and Sarah Zubairy(2014), “Government Spending Mul-
tipliers in Good Times and in Bad: Evidence from 20th Century Historical
Data,” November 2014 working paper.
Romer C. and D. H. Romer (2010), “The Macroeconomic Effects of Tax
Changes: Estimates Based on a New Measure of Fiscal Shocks”, American
Economic Review, 100(3), 763—801.
Schmitt-Grohe, S. and Uribe, M. (2012). ‘What’s news in business cycles’,
Econometrica, vol. 80(6), pp. 2733—64.
Uhlig, Harald (2005): “What are the Effects of Monetary Policy? Results
from an Agnostic Identification Procedure” Journal of Monetary Economics.
Uhlig, Harald (2012), “Economics and Reality,” Journal of Macroeco-
nomics 34 (March 2012): 29-41.
36
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18 20
Tax
(pe
rcen
t)
quarter
Tax shocks with sample 1978q1 2012q4
-2
-1
0
1
2
2 4 6 8 10 12 14 16 18 20
Tax
(pe
rcen
t)
quarter
Expenditure shocks with sample 1978q1 2012q4
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18 20
Spen
ding
(pe
rcen
t)
quarter
Tax shocks with sample 1978q1 2012q4
-2
-1
0
1
2
2 4 6 8 10 12 14 16 18 20
Spen
ding
(pe
rcen
t)
quarter
Expenditure shocks with sample 1978q1 2012q4
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18 20
Out
put (
perc
ent)
quarter
Tax shocks with sample 1978q1 2012q4
-2
-1
0
1
2
2 4 6 8 10 12 14 16 18 20
Out
put (
perc
ent)
quarter
Expenditure shocks with sample 1978q1 2012q4
Estimated Impact of tax and expenditure shocks in SVAR model
Figure 2: Impulse response functions to Tax and Spending Shocks with SVAR (Blanchard,
Perotti 2002)
37
-8
-6
-4
-2
0
2
4
0 1 2 3 4 5 6 7 8 9 10 11
perc
ent
quarter
Tax plans with sample 1978q1 2012q4
-8
-6
-4
-2
0
2
4
0 1 2 3 4 5 6 7 8 9 10 11
perc
ent
quarter
Spending plans with sample 1978q1 2012q4
Estimated Impact of TB and EB plans on Output growth in MA model
Figure 3: Impulse response function of output growth using truncated moving average
with plans (Favero, Karamysheva 2015)
38